Brightly burning rocks could be seen for hundreds of kilometres as they crashed into the Ural region.
Chelyabinsk residents reported shaking ground, windows being shattered and car alarms being set off during the shower.
The traces from falling objects could be seen in Yekaterinburg, about 125 miles south-east of Chelyabinsk, a witness told the Reuters news agency.
At least 100 people – many injured by broken glass – have been taken to hospital for treatment, medical officials in the city have said.
A witness in Chelyabinsk told Reuters that a huge blast was heard early on Friday morning and that shockwaves were felt in a 19-storey building in the town centre.
The Interfax news agency said that preliminary reports indicated that four people were injured by flying glass.
People in the Chelyabinsk and Sverdlovsk regions reported seeing “burning objects” in the sky, which also fell on the cities of Yekaterinburg and Tyumen – a sparsely populated area of about 310 miles.
About 600 sq m (6,000 sq ft) of a roof at a zinc factory collapsed, the Associated Press quoted an interior ministry spokesman as saying.
The Chelyabinsk region is Russia’s industrial heartland, an area that has many factories, a nuclear power plant and the Mayak atomic waste storage and treatment centre.
The emergencies ministry said that thousands of rescue workers had been dispatched to the area to provide help to the injured.
Officials say that the shower began after a large meteorite disintegrated above the Urals mountain range and partially burned up in the lower atmosphere – resulting in fragments falling earthwards throughout the Chelyabinsk region.
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